{"paper":{"title":"Spectral Inequalities for the Schr{\\\"o}dinger operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gilles Lebeau (JAD), Iv\\'an Moyano (DPMMS)","submitted_at":"2019-01-11T08:50:50Z","abstract_excerpt":"In this paper we deal with the so-called \"spectral inequalities\", which yield a sharp quantification of the unique continuation for the spectral family associated with the  Schr\\\"odinger operator in $ \\mathbb{R}^d$ \\begin{equation*} H_{g,V} = \\Delta_g + V(x), \\end{equation*} where $\\Delta_g$ is the Laplace-Beltrami operator   with respect to an analytic metric $g$,  which is a perturbation of the Euclidean metric, and $V(x)$ a real valued analytic potential  vanishing at infinity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.03513","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}